The primary task of a longitudinal differential protective relay comprises providing
a clear and rapid discrimination between faulty and faultless conditions PA1 a clear discrimination of fault zones of a transmission line PA1 a clear discrimination of a faulty phase. PA1 measuring phase current and phase voltage at each terminal PA1 making a Fourier series expansion of measured phase quantities with the aid of a parameter estimator and a frequency estimator, corresponding to the technique described, inter alia, in U.S. application Ser. No. 241,370 ("Frequency relay") PA1 producing the residuals of the phase currents and phase voltages with signs (according to equation (11)) PA1 producing the value of corresponding loss functions (according to equation (5)), and PA1 adapting the time between the samplings so that the number of sampling points is constant, independently of any frequency variations.
The classical and predominant technique for imparting these properties to a longitudinal differential protective relay is based on the fact that the vector sum of corresponding terminal currents at the two ends of a protected line zone is to be zero when the line is in a faultless condition and that a possible vector sum is equivalent to the fault current when a fault has occurred on the line.
To be able to carry out the vectorial summation between currents at different terminals belonging to the protective system of a power transmission line, some form of communication facility between the terminals is required. The present technique for communication comprises the use of so-called metallic pilot wires, largely disposed parallel to the transmission line to be protected. Unfortunately, this technique often limits the use of current comparison protective devices to relatively short transmission lines. According to Kirchhoff's laws, the general rule applies that the amount of supplied current is equal to the amount of discharged current. For transmission lines, this is quite correct for shorter line distances. On longer lines, however, capacitive charging currents occur which may have an influence on the measurement result. To limit the effect of these, according to the prior art the line distances for a protective zone are maximized, for example so that the charging current shall be less than a certain value of the primary current of the measuring current transformers. With the present technique, this requirement entails that a protective zone seldom exceeds 20 km.
In addition to the above-mentioned primary requirements on a longitudinal differential protective relay, they should also be stable, i.e. they shall not indicate a fault in the case of large surge currents passing through the line, in the case of power swings, and in the case of extreme load conditions.
As will have been clear from the above, there are a number of technical problems to be solved in connection with the embodiment of a longitudinal differential protective relay. Therefore, it is also desirable and necessary to obtain such protective relays with performance and properties superior to those offered by the classical analog technique.
In the field of protective relays, numerical technique with computer controlled systems have come into use in recent years. This is also true of the field of longitudinal differential protective relays. A new technique has also been applied for the necessary communication between the terminals, for example in the form of communication concepts operating over telephone frquency or wide-band communication links, optical conductors, etc.
A longitudinal differential protective relay according to the invention is based on the achievements made through the use of numerical technique and computer controlled systems. Based on these techniques a large number of concepts are available for solving the specific problems which are associated with longitudinal differential protective relays.
The general base for these computer controlled and numerically working protective relays comprises using measured values of the quantities in question, as a rule phase currents and phase voltages, for obtaining unknown system parameters of mathematical models of the measured signals. By regarding the measured signals as stochastic variables, theories from signal processing and statistics can be applied for estimating the unknown system parameters in the signal models. The parameters may be Fourier coefficients, mean values or line parameters. A parameter estimating protective relay offers new possibilities of realizing known protective relay principles, which means that they permit a general solution of the measurement function for protective relays.
The advantage of a parameter estimating protective relay is chiefly that the protective relay becomes an adaptive filter, in which the accuracy of the estimated parameters can be controlled to the desired level. In the case of transients, information about model faults as well as parameters can be utilized, which leads to both transient-measuring and steady-state measuring functions.
There are many ways of realizing parameter estimators and longitudinal differential protective relays based on this technique. A number of reports describing the prior art will be described in the following.
W. S. Kwong et al, at the IEE Power System Protection Conference, April 1985, London, presented a microcomputer-based current differential protective relay for transmission lines having two or more end points. This protective relay is characterized by a function image of about 30 ms, has separate comparison of phase and amplitude for the currents, has continuous supervision and measurement of the time delay of the communication channel as well as compensation for variable delay time on the channel.
Yamaura et al, at the IEE Power System Protection Conference, March 1980, London, presented a publication entitled "FM Current-Differential Carrier Relaying". According to the model described, the instantaneous currents at each terminal are modulated to frequency signals within the frequency band for voice-frequency signals, i.e. 300-3400 Hz. These signals are transmitted to other terminals via communication links such as microwaves and optical fibres. Otherwise, this protective relay is characterized in that it is bassed on semiconductors, has separate detection of phases for both phase-to-phase faults and phase-to-ground faults, has an operating time related to 60 Hz of 12-16 ms and in that the phase comparative system is dependent on suitable communication links to transmit the frequency-modulated carrier wave.
Aggarwal et al, at the IEE Power Protection Meeting, April 1985, London, presented a publication entitled "High Speed Differential Protection of Teed Circuits Using Wideband Communication Techniques". This describes the bases of a fast, differential current-based concept for T-shaped supply lines based on the master/slave technique and using a fibre-optic link as means of communication. The fundamental mode of operation is based on deriving a differential quantity and a bias quantity by using the instantaneous values of modally converted currents at the three ends of the T-shaped circuit. The use of modally transformed currents instead of phase currents increases the stability of the relays in faultless circuits when being applied to double lines. This relay design has arisen from a series of CAD studies.
In summary, it can thus be said that the principle of relays with differential currents is well-known and simple. Kirchhoff's fist law is used for a transmission circuit and the sum of the terminal currents has to be equal to the charging current in the circuit. A simple vector summation of the terminal currents, however, is not sufficient for a protective relay, since a minor fault when estimating the terminal currents when there is a heavy load could result in the determination of an internal fault.
In addition to the general description made above regarding the principles of computer-based protective relays and protective relays based on mathematical models as well as the description of a number of published concepts, a short reference will also be made of the methods for estimation of the parameters which are used in a longitudinal differential protective relay according to the invention. These methods are described in detail in U.S. application Ser. No. 212,225, filed June 27, 1988 ("Frequency relay") and comprises transforming a measured signal obtained from the network, after filtering and digitization, into an analytical model in the form of a truncated Fourier series expansion. The Fourier coefficients are determined in a parameter estimator operating with an estimation method in accordance with the least squares method. Starting from model values, according to this concept a computation of the frequency can be performed in a frequency estimator, the output signal of which is partly returned as the actual frequency value to the parameter estimator and partly constitutes a measure of the actual frequency. This part of the frequency relay according to U.S. application Ser. No. 212,225 is incorporated in the longitudinal differential protective relay according to the present invention. The parameter estimation in question is clear from the following. The measured signals in question can be modelled as follows: ##EQU1## which can be transformed to EQU y(t)=.theta..sup.T .phi.(t) (2)
where EQU .theta..sup.T =(a.sub.0, -a.sub.0 b.sub.0, c.sub.1 cos d.sub.1, c.sub.1 sin d.sub.1, . . . c.sub.N cos d.sub.N, c.sub.N sin d.sub.N) (3)
is a parameter estimation vector and EQU .phi.(t)=(1, t, sin .omega..sub.0 t, cos .omega..sub.0 t, . . . sin N.omega..sub.0 t, cos N.omega..sub.0 t) (4)
is a regression vector.
Estimation of the parameters according to the least squares method entails minimizing the value of a "loss function" V.sub.N. VN can be written as ##EQU2## where .lambda. is a forgetting factor and where .epsilon.(t) is an estimation error function.
The minimization gives the following equation for .theta.(t) ##EQU3##
The actual estimation is performed recursively with the aid of the following algorithm EQU R(t)=.lambda..multidot.R(t-1)+.phi.(t).phi..sup.T (t) (7) EQU R(0)=.delta..multidot.I (8) EQU R(t)L(t)=.phi.(t) (9) EQU y(t)=.theta..sup.T (t-1).phi.(t) (10) EQU .epsilon.(t)=y(t)-y(t) (11) EQU .theta.(t)=.theta.(t-1)+L(t).epsilon.(t) (12)
Here, R(t) is the covariance matrix of the regression vector and P(t) according to the below constitutes the inverse thereof. Otherwise, the following recurrence formulae are used EQU r(t)=P(t-1).phi.8t) (13) EQU d(t)=.lambda.+.sup.T (t)r(t) (14) EQU L(t)=r(t)/d(t) (15) EQU P(t)=(P(t-1)-r(t)L.sup.T (t))/.lambda. (16) EQU P(0)=(1/.delta.).multidot.I (17) EQU .theta.(0)=.theta..sub.0 ( 18)
One problem in connection with longitudinal differential protective relays using several terminals is to relate the measured signals, in a distributed area of protection, to the same points in time. One method that has been used comprises detecting the zero crossings of the measurement signals, but for multi-terminal networks this is not a particularly reliable method for different reasons. In these situations, instead, a different method is used which is based on optical communication and transmission of special synchronizing impulses.
In an article published at the Proceedings of the American Power Conference, Chicago, Apr. 24-26, 1984, entitled "The application of synchronous clocks for power system fault location, control and protection, pp. 437-447, by J. Esztergalyos, D. C. Erickson and J. N. Andres, a method of synchronizing measurement at several locations with the aid of synchronizing impulses from satellite clocks is described. This technique is applied for synchronized measurement/sampling in longitudinal differential protective system according to the invention. The method will be described in more detail with reference to the further description of the invention.
As will be clear from above, in connection with longitudinal differential protection it is very important to have access to a good communication channel between the terminals included in the protective system. When a protective system is based on computer and numerical technique, it is self-evident that also the communication is carried out with the same technique. The development within the fibre optics and also conventional carrier wave systems nowadays permit high-quality communication and the possibility of a relatively high information flow. However, a limiting factor for the amount of information is the band width of the communication channel. Using today's technique this means that the signal transmission capacity is limited to 64 kbit/s.
When transmitting three-phase current residuals, it can be shown that a smallest speed of communication of 36 kbit/s is required. In addition to these measured values, transmission requirements for check bits, possible absolute value information, protocols, and the like, are to be added. By using some code compression technique, noise and large signal values can be reduced. Taken together, however, the necessary amount of information comprises a transmission requirement which lies within the scope of the available, i.e. 64 kbit/s.
The basis of the fault location, both as regards line zone and phase, is described in U.S. application Ser. No. 241,370, filed Sept. 7, 1988 ("High resistance ground fault protection"). Knowledge of the direction to a fault can be obtained by studying the polarity of the current residuals after the occurrence of a fault. The condition for this is that there are terminals on both sides of the line zones in question and that there are communication facilities between the stations. The general rule is then that if the currents at both measuring points are directed away from the protected zone, the signs of the instantaneous residuals in the faulted phases at the respective measuring points are to be the same if the fault has occurred within the zone. The same criterion of the sign also applies if both currents are directed towards the interior of the protected zone. The fault is also present within the protected zone when the signs are different and when the current at one measuring point is directed towards the interior of the protected zone and the current at the other measuring point is directed away from the measuring point. The sign is determined by integrating the residuals during a certain time from the instant of the fault.
By studying the loss function or the amplitude of the harmonics, information can be obtained as to which of the phase or phases has or have faulted.